论文标题
mod $ p $ hilbert模块化表格的最小重量锥
The cone of minimal weights for mod $p$ Hilbert modular forms
论文作者
论文摘要
我们证明，所有mod $ p $ hilbert模块化形式都是通过繁殖的综合部分hasse不变的形式而产生的，这些形式的重量落在某个最小锥体之内。这回答了Andreatta和Goren提出的一个问题，并概括了我们以前的结果，该结果处理了$ P $在完全真实领域中不受影响的情况。尽管我们以前的工作利用了Goren-oort分层的深jacquet-langlands类型结果（当$ p $分层时尚不可用），但在这里，我们在iwahori级别使用分层的属性，这些属性更容易被其他Shimura品种推广。
We prove that all mod $p$ Hilbert modular forms arise via multiplication by generalized partial Hasse invariants from forms whose weight falls within a certain minimal cone. This answers a question posed by Andreatta and Goren, and generalizes our previous results which treated the case where $p$ is unramified in the totally real field. Whereas our previous work made use of deep Jacquet-Langlands type results on the Goren-Oort stratification (not yet available when $p$ is ramified), here we instead use properties of the stratification at Iwahori level which are more readily generalizable to other Shimura varieties.
